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%% section 5 What about (BFKL) Hard Diffraction? [slac-pub-7096-0-0-5 in slac-pub-7096-0-0-5: slac-pub-7096-0-0-6]
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\section{\usemenu{slac-pub-7096::context::slac-pub-7096-0-0-5}{What about (BFKL) Hard Diffraction?}}\label{section::slac-pub-7096-0-0-5}
The first mechanism for the small-$x$ dynamics which was discussed
in Section 2, i.e. ``color-transparency" or ``QCD Bethe-Heitler" (or
noncollinear photon-gluon fusion), must at some level also be
present. For the reasons already cited, I suspect it is at no more
than the 10\%--20\%\ level. But that is only a guess. The best way
to isolate it experimentally is via the 3-jet final state morphology
exhibited in Fig. \docLink{slac-pub-7096-0-0-2.tcx}[fig2]{2}. This is the seed kernel for building
at high energies and fixed $Q^2$ the BFKL $W^2$ dependence
\cite{18} via production of extra gluons into the phase space,
gluons typically also carrying $p_T$ of order $\sqrt{Q^2}$. The
$W^2$ dependence to be expected is much stronger, of order
$(W^2)^{0.4}$.
Open questions regarding the relevance of this mechanism for HERA
include
\begin{enumerate}
\item
whether the normalization of the lowest-order kernel is large enough,
\item
how much room there is in the available HERA phase space for
building up the power-law behavior, and
\item
whether the scheme is consistent: there exist criticisms regarding
``diffusion into the infrared", as well as claims
\cite{19,20,21,22} that more careful attention must be paid to
energy-conservation constraints within the multi-Regge kinematics.
\end{enumerate}
\vspace{.5cm}
\begin{figure}[htbp]
\begin{center}
\leavevmode
\epsfxsize=5in
\epsfbox{8117A03.eps}
\end{center}
\caption[*]{A log-log sketch of $F_2$ vs $Q^2$ at various fixed values
of $W^2$.}
\label{fig3}
\end{figure}
\noindent
An observed trend toward the BFKL $W^2$ dependence would clearly be
of fundamental importance, implying a new class of nonperturbative,
absorptive effects going far beyond those we used in the previous
section to interpret existing data. I here make only the most modest
suggestion, regarding how to plot the data. I am a firm believer in
the importance of searching for the optimum way of presenting data,
the way which most directly highlights what is important. My
suggestion in this case is to plot log $F_2$ versus log $Q^2$ at
fixed $W^2$. A sketch of what I mean is shown in Fig. \docLink{slac-pub-7096-0-0-5.tcx}[fig3]{3}.
$W^2$ is chosen rather than $x^{-1}$ because there is no longer
scaling in the small-$x$ region, and because the nonscaling depends
on gluon emission, which probably is more dependent on the amount of
available phase space than anything else. (This is certainly the case
for BFKL). The logarithmic scales allow a clear view of how the
photoproduction limit is approached, and above that limit by some
not-so-well-defined factor is the Gribov bound, unmodified by any
damping due to color-transparency or aligned-jet configurations.
Existing data for not large $W^2$ show a curve of log $F_2$ vs log
$Q^2$ which is concave down. If any part of the curve becomes at
high $W^2$ concave up, this would be to me a signal for ``BFKL
behavior", because it is the only way the Gribov bound can be
reached. The important regime for HERA is, as is well-known,
moderate $Q^2$ (0.5 GeV$^2$--15 GeV$^2$) at the highest $W^2$
attainable.
My own favorite guess \cite{23} on how things will turn out
is that the curves will remain concave down, but that the $W^2$
dependence of the maximum of $F_2(Q^2, W^2)$ for given $W^2$ will
behave more or less like BFKL.
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